Sizing up spotted lanternfly nymphs for instar determination and growth allometry

A major ongoing research effort seeks to understand the behavior, ecology and control of the spotted lanternfly (SLF) (Lycorma delicatula), a highly invasive pest in the U.S. and South Korea. These insects undergo four nymphal stages (instars) before reaching adulthood, and appear to shift host plant preferences, feeding, dispersal and survival patterns, anti-predator behaviors, and response to traps and chemical controls with each stage. However, categorizing SLF life stage is challenging for the first three instars, which have the same coloration and shape. Here we present a dataset of body mass and length for SLF nymphs throughout two growing seasons and compare our results with previously-published ranges of instar body lengths. An analysis using two clustering methods revealed that 1st-3rd instar body mass and length fell into distinct clusters consistently between years, supporting using these metrics to stage nymphs during a single growing season. The length ranges for 2nd-4th instars agreed between years in our study, but differed from those reported by earlier studies for diverse locations, indicating that it is important to obtain these metrics relevant to a study’s region for most accurate staging. We also used these data to explore the scaling of SLF instar bodies during growth. SLF nymph body mass scaled with body length varied between isometry (constant shape) and growing somewhat faster than predicted by isometry in the two years studied. Using previously published data, we also found that SLF nymph adhesive footpad area varies in direct proportion to weight, suggesting that footpad adhesion is independent of nymphal stage, while their tarsal claws display positive allometry and hence disproportionately increasing grasp (mechanical adhesion). By contrast, mouthpart dimensions are weakly correlated with body length, consistent with predictions that these features should reflect preferred host plant characteristics rather than body size. We recommend future studies use the body mass vs length growth curve as a fitness benchmark to study how SLF instar development depends on factors such as hatch date, host plant, temperature, and geographic location, to further understanding of life history patterns that help prevent further spread of this invasive insect.


Introduction
The spotted lanternfly (SLF), Lycorma delicatula White (Hemiptera: Fulgoridae) is a planthopper native to south Asia that has become a highly invasive pest in the U.S. and South Korea. SLFs feed intensively on phloem from a wide variety of trees and other plants, stressing the hosts as well as promoting the growth of sooty mold (1). Because SLFs threaten significant economic damage to agricultural crops, native trees, and landscape plants, a large ongoing research effort seeks to understand their development, physiology, behavior and ecology to inform methods for mitigation and control (2)(3)(4). In this study, we discuss how clustering methods can be applied to measurements of the body mass and size of immature SLFs (nymphs) in order to improve the determination of SLF life stage and to study the scaling of previously published SLF footpart and mouthpart dimensions (5) with body size. We begin by explaining how these issues are relevant to a wide variety of topics in SLF research.
After emerging, SLFs develop through five life stages separated by molting: four nymphal instars and the much larger and winged adult stage. The 4th instars are readily identified by their distinctive red, black and white spotted coloration. However, the first through third instars have similar black-and-white-spotted coloration and overall body morphology (Fig 1). Many studies of SLF behavior, ecology, and phenology have relied on determination of the nymphal stage (instar determination) in order to track how life stage influences ecology and choice of host plants (1,2), dispersal patterns (3)(4)(5)(6), locomotor behaviors such as climbing and jumping (7,8), phenology and activity (9), spectral preferences (10), attraction to chemicals (11), and effectiveness of various trapping methods (12). Thus, instar determination methods for identifying the life stage of a given specimen collected in the field are useful and important in many contexts. Several previous studies have shown how a detailed microscopic examination can reveal foot, mouth part and antenna morphological changes during development (7,13,14), providing information of great utility for how these factors influence feeding, adhesion and locomotion throughout the insect's life cycle. In practice, the life stages of the first three SLF instars have been estimated in many studies using overall body dimensions readily measured in the field, along with previously published size ranges for each instar.
In spite of this growing interest, only a few previous studies have reported measured data for the ranges of body lengths corresponding to each nymphal life stage for use in instar determination, and none have reported body mass. (Table 1, Fig 1) The earliest study reported only mean body lengths for each stage in China (15). Park and colleagues (16) measured body lengths for 1st through 4th instars in South Korea, although it was not stated whether specimens used for measurements were raised in the laboratory with known life stage or collected from the wild and the instar stage estimated from size. Jang et al. (10) reported only body lengths for just 2nd instars captured in the field in South Korea. Dara et al. (17) reported the ranges of body lengths measured for 1st through 4th instar nymphs collected in Pennsylvania. None of these previous studies provided statistical data to guide the classification of new datasets for instar determination. Furthermore, studies have shown that the size ranges for each instar can depend on factors such as date of emergence, diet, host plants, temperatures, and environment (e.g., laboratory vs field-raised) (18). Indeed, prior research has indicated that SLF nymphs develop and survive differently when reared with different diets in the field (19,20), at different temperatures (21), and artificial conditions (i.e., enclosures or laboratory conditions) (1,16), but these studies did not consider how these factors affected instar morphometrics. For many insects and other arthropods, instar determination (i.e., identifying the life stage of nymphs collected in the field) relies on the observation that major changes in body dimensions occur primarily when the exoskeleton is shed upon molting (18). Ideally, this involves directly measuring the frequency distribution of one or other metrics of exoskeleton size for each instar using laboratory-reared specimens with known molting status (e.g., based on molted head capsule dimensions) (22). However, instar determination should be possible without knowledge of molting status if the number of developmental stages is known in advance, the morphometric data is uniformly sampled across all life stages, and its frequency distribution is partitioned into distinct clusters (23). The last approach is especially useful for SLFs, which have proven challenging to raise in the laboratory so that life stage can be directly monitored (20,21), and which we have observed to have flaccid cast exoskeletons that do not provide useful sizing information after molting.

th instar
In this study, we report measurements of mass and body length for spotted lanternfly nymphs along with clustering results for these specimens. By comparing these results with those from four previous studies, we explore the variation in SLF nymph size distributions reported thus far.
A growth (ontogenetic) allometric analysis was also performed to identify possible adaptations for feeding morphology and biomechanics. Body mass has been found to scale as a power law of body length (i.e., M = L c ) for a wide range of insect and other arthropod taxa with scaling exponents c that vary from < 1 to 3 (24), where c = 3 corresponds to isometric growth (geometrical similarity; maintaining a constant shape), c > 3 to positive allometry (i.e., growing faster than predicted by isometry) and c < 3 to negative allometric growth (i.e., growing more slowly than predicted by isometry). We used our data to determine the ontogenetic scaling regime of SLF nymph body mass, and use previously-published morphometric data to determine how the dimensions of foot and mouth body parts scale with overall body size. We interpret these results in relation to SLF behavior and ecology, and suggest ways these methods can be applied in future work.

Insect collection and morphometrics
Healthy, intact SLF nymphs were collected in the field from Ailanthus altissima trees and wild grape vines (Vitis spp.) in southeastern Pennsylvania (40°00'30.2"N 75°18'22.0"W) from May through July, 2021 and 2022, corresponding to 1st instar emergence until it was difficult to find 4 th instars (note this was a different date in the two years). In both years, we measured all specimens collected from the field site using an insect net to avoid sampling bias. Details on the collection timeline and number of specimens collected, which corresponded to multiple samples per instar (2-4 weeks/stage in 2021; 4-5 weeks/stage in 2022) are given in S1 Appendix. A total of N = 194 (2021) and N = 226 (2022) specimens were collected across all nymphal life stages (Table 1). Because SLF are identified as an invasive species in Pennsylvania, all specimens were euthanized by freezing (25). Morphometric data were measured post-mortem after thawing for 15 min to preserve tissue hydration and morphology using an analytical balance (Explorer, Ohaus, Parsippany, NJ US) to measure mass, M (accuracy ± 0.4 mg). Body length, L, was defined as distance between the anterior end of the head to the posterior end of the abdomen; it was measured using ImageJ (26) to ± 0.05 mm from digital micrograph images of specimens lying flat on their dorsal or ventral surfaces with a scale bar in the same plane. Micrographs taken from a variety of perspectives indicated that the effect of specimen orientation was ≤ 4% of body length and hence ≤ measurement uncertainty.

Comparison with other studies
We performed Google Scholar searches using the keywords spotted lanternfly and Lycorma delicatula, yielding over 600 references. Approximately 100 papers that directly studied SLFs were used to perform repeated forward and reverse citation searches to find morphometric data for spotted lanternfly nymphs. This resulted in the identification of four papers with additional values of body length (10,(15)(16)(17). We also found one study that reported adult SLF body length and mass, which agreed with our own observations (27 All 4th instars were identified by their red, black and white coloring. Length and mass data for all specimens with black and white coloration consistent with 1st through 3rd instars were standardized before clustering by converting them into z-scores (i.e., zero mean and standard deviation = 1). For the first clustering method, the standardized data were fit to a three component Gaussian Mixture Model using fitgmdist (covariance type = full, shared covariance = false), then sorted into three components (clusters) using cluster in MATLAB to reflect the known number of instar stages in the dataset. We also partitioned only the length data for the first, second and third instars into three clusters using the Gaussian Mixture Model and kmeans for k-means clustering.
We next analyzed the mean lengths for each estimated instar to determine whether they follow Dyar's Rule, the observation that instar body dimensions increase in size by a constant growth ratio between successive instars (28) This implies that log Lj = j × log G + log L0, where j = instar number, L j = mean body length of the jth instar, and G = growth ratio = Lj+1 / L j (18). We used simple ordinary linear regression (MATLAB fitlm) to fit body length data from this study and previous work vs estimated instar number; we also computed as goodness-of-fit measures the F-statistic and p-value for significance testing (alpha = 0.05; null hypothesis no dependence on the independent variable), and R-squared. We used MATLAB confint to find 95% CI of all fit parameters. To fit body length data from previous studies, we used either means or middle of the quoted range, depending on which statistics were provided. (Table 1) To determine the power law dependence of body mass on body length (i.e., M = a L c ), we first log-transformed the M and L data, and then used simple ordinary linear regression to fit to log M = a + c log L, as described above. The fitted slope (the scaling exponent, c) was used to determine whether these data were consistent with the null hypothesis of isometric scaling (i.e., c = 3), or instead with positive or negative allometry. (See full results in S4 Appendix).
We performed the same analysis for tarsal claw and mouthpart (stylet and labium) dimensions from a previous study (14) vs body length to test for agreement with power law scaling with body length, and isometric scaling(c = 1) in particular. Because scaling law fits to both mouthpart lengths vs body length did not include any adult data within the fit confidence intervals, we also performed fits to only the data for nymphs.
Previous research has found that the adhesive pad area, A adh , scales linearly with body mass for organisms over a wide range of taxa and body sizes (29). For comparison, isometric scaling predicts that Aadh ∝ L 2 ∝ M 2/3 . We therefore tested whether either of these relationships hold for SLFs using published data for their arolium dimensions (14) to estimate the arolium area (S2 Appendix); we then performed scaling law fits to these data vs body mass using the methods described above. Because the arolium does not increase monotonically in size (i.e., it is smaller on average for adults than for 4th instars) we fitted only the values for nymphs.

Instar determination
The results of our morphometric measurements are shown in Fig 2 along with clustering data using the GMM model for mass vs body length. (See full results in S3 Appendix.) The data were sorted into identical clusters using GMM clustering for mass vs length and using k-means on lengths only. The cluster centroids provide estimates for the mean body length and mass for each life stage, which we compare with earlier studies in Fig. 3. As can be seen in Fig. 3A and Table 1, the body lengths for each instar agreed closely for the two years studied here, but not with values from earlier studies. The body masses were lower for early instars for the 2022 data than for those in the 2021 data, but greater for 4 th instars.  respectively, for each instar reported in previous studies (Table 1).

Fig. 3. Comparison of body length and mass for each spotted lanternfly nymph stage from this study and previous research. (A) Spotted lanternfly nymph body length vs instar
from this study and previous work (

Allometry
The SLF nymph body mass vs length data followed power law scaling with significantly different scaling exponents for the two years studied:  (Table S1, (29). (Fig 5B) By contrast, the fits shows that SLF nymph mouthpart dimensions (labium length, LL, and stylet length, LS) were only weakly correlated with body length (S4 Appendix, Fig 5B,C); i.e., power law scaling explains only 36% of the total variance in these data. confidence intervals from ordinary linear regression fits to power laws, as described in the main text.)

Discussion
The results of this study lead to several conclusions. First, the distribution of measured data for body mass and length for 1 st to 3 rd instars were consistent with three non-overlapping clusters of data in the approximate size ranges expected for these life stages from previous studies. We consequently used two methods to assign these data to three clusters: 1) GMM on both mass and length data; 2) k-means clustering applied to length-only data. Both methods resulted in identical cluster assignments. This indicates that easy-to-perform specimen body length measurements and k-means clustering should be sufficient for instar determination. Fourth, these data can be used to create new syntheses of existing research for greater insight into the biology of these insects. For example, Kim et al. (30) hypothesized that earlier SLF instars should be more easily dislodged by wind than later nymphs due to their smaller arolia, an idea with implications for how dispersal and control should depend on life stage. However, SLF nymph arolium area (the morphometric measure relevant for adhesive strength) from (14) was found to scale with extreme positive allometry with body length and mas, in agreement with the scaling relationship found across taxa over 7 orders of magnitude of body weight (29). In combination with the finding of constant (i.e., size-independent) maximum adhesive stress between the arolium and surface for other insect adhesive pads (e.g., the pulvilli of Coreus marginatus (30) and the arolia of stick insects in (31) By contrast, the analysis showed that the variation in the stylet and labium lengths was only weakly correlated with body length for SLF nymphs (14). This is consistent with the expectation that stylet length is correlated with preferred host plant tissue characteristics (33), as opposed to insect size, given reports from the literature indicate that SLF nymphs only feed on herbaceous and non-woody parts of plants (e.g., shoots, stems and leaves) while adults are able to feed on bark-covered trunks (7,9,16,17,34).

Conclusion
We propose that body mass vs length curves can play a role similar to that of clinical growth charts, filling the current gap in metrics of SLF development. These measures can serve as a fitness benchmark for interpreting data from field studies and laboratory experiments to assess the impact of factors such as date of first emergence, molt schedule, temperature, diet, and geographic location. Furthermore, the successful fits to Dyar's rule provide a measure of the growth ratio between successive instars, which might serve as an additional metric for comparing populations grown under different circumstances. Another potential use of these methods involves estimating the life stage of isolated SLF nymphs found in new locations as these insects expand their range. This information can play a valuable role in determining the stage of infestation, informing control efforts as well as providing data useful for tracking and modeling their spread. We therefore suggest that morphometrics of SLF nymphs be incorporated into ongoing studies when possible so as to provide a wide range of data for such applications going forward. S1 Appendix. Sampling timeline for spotted lanternfly nymph body length and mass S1 We used the data from Table 5 in (1) for spotted lanternfly arolium (foot adhesive pad) dimensions using the approximately triangular geometry defined in Fig 1 in ref. (1). This gives an estimated arolium area, Aadh: where the relevant arolium dimensions are defined in S2 Fig and S2 Table below.
S2 Table. Definitions of labels for arolium dimensions.